
In OS-CS, \(h_n(u)\)  in Eq. (REF ) is expressed by[1]}
\(h_n(u)=\lambda _n(1+u)^{-\frac{n_j}{2}}, \ \ \lambda _n=\sqrt{\frac{n_j!}{n!(n_j-n)!}},\) 
where \(n_j\)  is a positive integer. For \(n>n_j\) , every \(h_n(u)\)  equals to zero.

In BG-CS, \(h_n(u)\)  in Eq. (REF ) is expressed by[2]}
\(h_n(u)=\frac{\lambda _n}{\sqrt{\mathcal {N}_{BG}(u)}}, \ \ \lambda _n=\sqrt{\frac{\Gamma (2\chi )}{n!\Gamma (2\chi +n)}}.\) 
Here, \(\chi \)  is a real number such that \(\chi \ge 1/2\) , \(\Gamma (\cdot )\)  is a Gamma function, and \(\mathcal {N}_{BG}(u)\)  is a normalization function defined by
\(\mathcal {N}_{BG}(u):=\Gamma (2\chi )u^{\frac{1}{2}-\chi }I_{2\chi -1}(2\sqrt{u}),\) 
where \(I_{\nu }(\cdot )\)  is a modified Bessel function.

In mSG-CS, \(h_n(u)\)  in Eq. (REF ) is expressed by[3]}
\(h_n(u)=\sqrt{\frac{n+1}{\mathcal {N}_{mSG}(u)}}\frac{1}{u^{\frac{n+1}{2}}}J_{n+1}(2\sqrt{u}).\) 
Here, \(J_n(\cdot )\)  is a first kind of Bessel function, and \(\mathcal {N}_{mSG}(u)\)  is a normalization function defined by
\(\mathcal {N}_{mSG}(u):=\frac{1}{u}\left[2u\lbrace J_0(2\sqrt{u})\rbrace ^2-\sqrt{u}J_0(2\sqrt{u})J_1(2\sqrt{u})+2u\lbrace J_1(2\sqrt{u})\rbrace ^2\right].\) 

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